In the context of educational measurement, statistical models are developed that relate the ability of a student to the probability with which a correct response to particular questions is given. Such models are refered to as Item Response Theory models. We consider an illustrative example where different researchers analyze the same data with different instances of the same measurement model. One researcher reaches the conclusion that students guess, whereas the other one concludes that students do not guess. Both models are shown to be statistically equivalent, and the example shows precisely where and how the beliefs of researchers have an effect on their respective substantive conclusions. We consider this problem in relation to the use of statistical models for scientific research.